Next Steps in Implementing
Mathematics (and Science)
Initiatives at the National and
State Levels: Focusing on
Common Core Standards
Jere Confrey, Joseph D. Moore University Distinguished Professor, Mathematics Education
Friday Institute for Educational Innovation, College of Education, North Carolina State University
U.S. Department of Education's Mathematics and Science Partnerships 2011Conference
February 15, 2011
Baltimore, Maryland
The instructional practices and assessments discussed or shown
are not an endorsement by the U.S. Department of Education
Common Core State Standards represent an
opportunity – once in a lifetime to form effective
coalitions for change
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
• The MSP programs can play a critical role in
maximizing this opportunity:
– To strengthen the movement towards Common
Core Standards implementation
– To get your innovations to move to scale to the
degree to which they can tie into a broader policy
agenda
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Features of the Common Core
• They focus attention on core concepts in number and
numeration and their relationships to operations with a focus
on the structure of the number system;
• Aggressive timelines for teaching particular concepts in
elementary and middle grades;
• They introduce multiple measurement systems (metric, nonstandard and English) simultaneously and tie the number line
directly to scales to improve students’ visualization of some
number relationships;
• They support the articulation of some key learning
trajectories in numeration and geometry; and
• They remain agnostic about sequencing and organization of
high school math.
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Decisions that Should Be Re-examined over time:
• The practices of mathematics are presented independently
from the content standards: the practices could be isolated
and under-emphasized without careful professional
development;
• There is limited detail to engaging students in mathematics
through modeling with robust use of technology, and
developing the related skills and concepts of modeling;
• New standards for Probability and Statistics in early grades
should supplant the current weak treatment of the topic in
Measurement;
• The CCSS construe Number narrowly tend to overemphasize
additive structures—limiting early and foundational
development of multiplicative/divisional structures related to
ratio and rate, and many algebraic patterns of growth;
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Nonetheless…
• Even with their flaws, the Standards are “good
enough” to embrace.
• There is a narrow window of opportunity to
prepare for and interpret the Next Steps.
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Window of Opportunity
• Window open from now until 2014- 2015 when assessments
are put into place.
• The current circumstance is unstable and ambiguous at the
state level:
– Example: NC has its third set of standards in three years; with 2001
assessments and 2008 assessment policy and membership in two
assessment coalitions and the passage of the CCSS. What should they
be telling teachers? What should they be doing on assessment?
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Goal for STEM education
• Schooling is about modeling our world
(scientifically, technologically,
mathematically, and statistically),
encouraging active citizenry, building
opportunities for expressiveness, fostering
collaboration, designing and testing
solutions, feeling engaged and empowered,
and being well-prepared to earn a satisfying
and sufficient living.
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Six Priorities around the
Instructional Core
Priority 4:
Professional
Development
Systems
Priority 1:
Phasing
Priority 2:
Linking
Assessment,
Curriculum
and
Instruction
Priority 3:
15% and
Literacy
Priority 5:
Curricular
Effectiveness
and Change
Priority 6:
Care and
Feeding of
Standards
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Priority One:
Phasing the Implementation
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Priority One: Phasing Implementation
Year
Grade Level
2010-11
K-1
2011-12
2-3
2012-13
4-5
2013-14
6-7
2014-15
8
and -- Include the mathematical practices
in all aspects of implementation.
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Phasing by Learning Trajectories
Posters of K-5, 6-8 and 9-12 CCSS in learning trajectories format
available at posters@wgen.net
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Phasing the Implementation
Simultaneously,
• new curricular development,
• general support systems,
• assessments,
• building technological infrastructure, and
professional development systems.
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Priority Two:
Smartly coupling curriculum
and classroom assessment
via the CCSS
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Priority Two: Smartly coupling curriculum and
classroom assessment via the CCSS
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Lack of Engagement
• Lack of engagement in learning is the greatest
problem in mathematics classes
• How do the CCSS help us with this?
– The Mathematical Practices as a way to leverage
discourse
– Formative Assessment or Assessment for Learning
– New technologies for networking
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Assessment for Learning
The UK Assessment Reform Group (1999) identifies
FIVE PRINCIPLES OF ASSESSMENT FOR LEARNING
1.
2.
3.
4.
The provision of effective feedback to students.
The active involvement of students in their own learning.
Adjusting teaching to take account of the results of assessment.
Recognition of the profound influence assessment has on the
motivation and self esteem of pupils, both of which are critical
influences on learning.
5. The need for students to be able to assess themselves and
understand how to improve.
Assessment for Learning Defined: Stiggins et al. (2005)
http://www.assessmentinst.com/wp-content/uploads/2009/05/afldefined.pdf
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Formative Assessment
…a process used by teachers and students during instruction
that provides feedback to adjust ongoing teaching and
learning to improve students’ achievement of intended
instructional outcomes.
1. rely on learning progressions (Heritage 2008)
2. share explicit learning goals
3. provide students with descriptive feedback
4. promote a collaborative environment
5. include peer and self assessments
(CCSSO, 2008)
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Defining Diagnostic Assessment
• Diagnostic Assessment requires an explicit theory of
how a student’s thinking progresses over time.
• Comes from a combination of dia, to split apart, and
gnosi, to learn, or knowledge
• Efficient, effective use of students’ responses, both to
document growth in their learning and
understanding (content and process) and to promote
that growth, from initial states to more powerful,
coherent and aligned conceptions
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Issues in Diagnostic Assessment
• Focus on big ideas in mathematics
• Focus on how children’s mathematics understanding evolves
over time, rather than replicating the ‘structure of
mathematics’
• Rapid feedback to teachers on individual and group status of
understanding
• Provide recommendations and interventions for improving
growth, remedying gaps in conceptual understanding
• Professional Development: continuous instructional
improvement
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
A learning trajectory/progression is:
…a researcher-conjectured, empirically-supported
description of the ordered network of constructs a
student encounters through instruction (i.e.
activities, tasks, tools, forms of interaction and
methods of evaluation), in order to move from
informal ideas, through successive refinements of
representation, articulation, and reflection, towards
increasingly complex concepts over time
(Confrey et al., 2009)
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Classroom Assessment
• Draws on students’ proclivity for interactions and
social networking
• Supplements teachers’ knowledge of student
thinking and content
• Reaches students directly to involve them in learning
• Supports reasonable levels of customization
• Builds on the base of knowledge of empirically
supported learning trajectories
• Supports rather than supplants curriculum
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Prototyping a Diagnostic Assessment
System: LPPSync
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Applets for Diagnostics
and Activities: Packet 1
Equipartitioning
Learning Trajectory
Proficiency levels:
1 (Collections)
3 (Justification)
4 (Naming)
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Priority Three:
Defining and deploying a broader college-andcareer STEM agenda by appropriating the
fifteen percent of a state’s standards that does
not have to comply with the CCSS;
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
What adoption means
• A state adopts 100% of the common core K-12
standards in ELA and mathematics (word for
word).
• With option of adding up to an additional 15%
of standards on top of the core.
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
ELA standards: Reading in Science and Technical
Subjects
Key ideas and details
Follow precisely a multistep procedure when carrying out experiments, taking
measurements, or performing technical tasks.
Reading Standards for Literacy in Science and Technical Subjects
Craft and Structure:
Determine the meaning of symbols, key terms, and other domain-specific words and
phrases as they are used in a specific scientific or technical context relevant to
grades 6–8 texts and topics.
Integration of Knowledge and Ideas:
Compare and contrast the information gained from experiments, simulations, video,
or multimedia sources with that gained from reading a text on the same topic
(grades 6-8)
Range of Reading and Level of Text Complexity
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Writing Standards for Science and Technical Subjects
• Text Type and Purposes
-- Write arguments focused on discipline-specific content
• Production and Distribution of Writing
– Develop and strengthen writing as needed by planning, revising,
editing, rewriting, or trying a new approach, focusing on addressing
what is most significant for a specific purpose and audience
• Research to Build and Present Knowledge
– Conduct short as well as more sustained research projects to answer a
question (including a self-generated question) or solve a problem; narrow or
broaden the inquiry when appropriate; synthesize multiple sources on the
subject, demonstrating understanding of the subject under investigation
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
• The math CCSS are conservative, and delayed on modeling,
probability and statistics, and rate of change and early
functions as an introduction to algebra.
• Further, they only modestly focus on the use of new learning
technologies: this could leave our students foundering in
exciting arenas incorporating visualization, integration of
topics, engineering, and design and the use of simulations.
These topics constitute a critical agenda for our field, and we
need a strategy to avoid their marginalization.
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Solution
•
•
•
•
argumentation,
reasoning,
weighing evidence, and
interpreting representations
Could be achieved by inclusion of simulations, dynamic displays,
and extensions of problems from informal and formal
contexts
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Trojan Horse Approach
Build innovative curricula for the 15% and for the Science and
Technical Reading and Writing Standards
Ways to implement:
a) Use school time that is often blank (inter-sessions, post
summative assessment time, near holiday time) and
b) Develop high school courses along the lines of “Theory of
Knowledge” in International Baccalaureate Programs
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Priority 4 : Developing advanced systems for
professional development around points 1-3;
• Professional development needs to be:
– Content and curricular specific
– Closely linked to classroom practices
– Include intensive learning opportunities with year round follow
up
– Obligatory
– Linked to building professional communities
• It needs to tie to standards, including their interpretation.
• States need professional development systems connecting district
resources, departments of public instruction and universities,
colleges and community colleges.
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Priority Five:
Using longitudinal data systems to decipher
and study curricular effectiveness and provide
empirical support for change.
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Priority Six: Using longitudinal data systems to
decipher and study curricular effectiveness and
provide empirical support for change.
On Evaluating
Curricular
Effectiveness
(NRC 2004)
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Recent Advances
• Implementation fidelity (Huntley, 2010)
• Opportunity to learn and related constructs
(McNaught et al. 2010)
• Fair Tests for comparison (Chavez et al. 2010)
• Complexity of relationships among teacher and
student variables and curricular effects Tarr et al.
(http://cosmic.missouri.edu/aera10/)
We need to continue to build on these to ensure that
we can substantiate future effectiveness
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Priority Six:
The Care and Feeding of the Standards
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
“Care and Feeding of the Standards”
• Should be an NRC type process with
documented responses to feedback
• Should include:
– members of professional organizations
– teachers
– researchers,
– assessment experts
• Should have a three part timeline: immediate
fixes, minor revisions and major reviews
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Conclusions
The Common Core State Standards present considerable
opportunities for innovative thinking around curriculum
 Require a plan for phasing in the CCSS by grades and
domains
 Need to elaborate the learning trajectories
 Need to inter-relate curriculum, instruction, and
assessment using new technologies as a priority to
improve engagement and fair opportunities
 Wise to expand our target to 15% and ELA
 Continue progress on evaluating curricular
effectiveness
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
• The success of the standards depends on the
ability of teachers to assist students in
learning the specified “fewer” standards at
grade level.
• Therefore, the success of the standards should
be measured heavily, though not exclusively,
on the narrowing of the performance gaps
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
“It is time to
recognize that
Standards are not just
promises to our
children, but
promises we intend
to keep.” CCSS 2010, p. 5
Photo: Tyler Confrey Maloney
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
“It is time to recognize that Standards are not just promises to
our children, but promises we intend to keep.” CCSS 2010, p. 5
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606
Friday Institute for Educational Innovation at North Carolina State University, Raleigh, NC 27606